24 capacitance and dielectrics

Question 1

What is a capacitor…

Answer 1

is a device that can be used to store electric charge and electric potential energy, it does this by insulting two conductors from each other. one conductor is given a positive charge and the other has an equal amount of opposite charge.

Question 2

Capacitance is ….

Answer 2

is the ability of a system to store and electric charge. In other words it is the ratio of charge in each conductor to the PD between the condutors

Question 3

A dielectric is …

Answer 3

a insulating material that can be placed between the conductors inorder to increase the capacitance. This occurs due to polarisation within the dielectric

Question 4

how to make a capacitor …

Answer 4

any two conductors separated by a vacuumed or insulating material form a capacitor. In order to charge the capacitor electrons are transferred form one conductor to the other. The two conductors gain an equal and opposite charge and the net charge over the capacitor remain constant.

Question 5

A way of charging the capacitor …

Answer 5

is to connect the two conducting plates to opposite terminals of a battery. The battery can then be dissconnected giving the capacitor a fixed PD.

Question 6

C = Q/V

Answer 6

this shows us that as the charge density doubles the electric field between the plates doubles. However the ratio of charge to voltage (PD) remains constant for a capacitor.

Question 7

The greater the capacitance of a capacitor ….

Answer 7

the more energy (charge) is stored per unit PD.

Question 8

the simplest type of capacitor is a ….

Answer 8

parallel plate capacitor. The conducting plates have a area A and are sepperated by distance d. The field between the plates is assentially uniform and the charge is unformly distributed over the plates.

Question 9

How to derive for a parallel plate capacitor

Answer 9

Question 10

What properties can we see about a capacitor form this

Answer 10

we can see that the capacitance of a parallel plate capacitor is inversely proportional to the distance betweent the plates and directly poportional to the area of the plates.

Question 11

What does this diagram show

Answer 11

the diagram shows 2 capacitors connected in series. When a constant PD is applied accross a and b the capacitor becomes charged, the charge on all of the plates in the diagram have the same magnitude. The top plate of C₁ aquires a positive charge Q. The electric fiels of the positive charges pulls the negative charges up to the bottome of the plate C₁. These negative charges cane for the top of plate C₂ which became postievely charged as a result. This pulls the negative charges form b to the bottom plate of C₂ so it becomes negitively charged. The total charge on the top of plate C₂ and the bottom of plate C₁ must be zero (or the same as the initial charge).

Question 12

equations for series combination

Answer 12

Question 13

What does the diagram show …

Answer 13

This diagram shows a arrangement of two capacitors in parrallel connected accross a and b. In the case of the upper plate of the capacitors C₁ and C₂ are connected to a current carryign wire that forms a equipotential surface, where the bottom plates form another. In other words the plates in this diagram have the same PD (where as in a series circuit the plates had the same charge), but they don’t have the same Q.

Question 14

equations for parallel combination

Answer 14

Question 15

What is the potential stored in a capacitor?

Answer 15

it is equal to the work done that is required to charge it. When the capacitor is discharged the stored energy is recovered a work done by electrical forces.

Question 16

How to find the Potential energy stored by a capacitor …

Answer 16

Question 17

Electric Field energy

Answer 17

We charge a capacitor by moving electrons form ine place to another. This requires work to be done against the electric field between the plates. Thus we can think of energy as being stored in the field in a region between the plates. to find teh energy per unit volume in a space between 2 parallel plates with an area A and seperation d we call this energy density denoted by u. Even thought the equation for u is derived form a parallel plate capacitor it applies for any electric field configuration in a vaccum.

Question 18

What are dielectrics made form?

Answer 18

electrically insulating matreials.

Question 19

Why do we use dielectrics?

Answer 19

1) They increase the maximum possible PD between the capacitor plates allowing for more energy to be stored per unit PD. Any insulating materail, when subjected to a sufficiently large electric field experiances a partial ionization that permits conduction through it. This phenomenon is called dielectric breakdown.
2) the capacitance of a capasitor of fixed dimentions is increased.
3) dielectrics allow us to have the conductors close together without touching.

Question 20

examples of dielectrics

Answer 20

waxed paper, polystryrene, parafin, dielectric glass.

Question 21

Dielectric constant

Answer 21

is denoted by K and is K = C/C₀ which equals the capacitance of a capacitor with a dielectric between the plates (C) over the capacitance of a capactior with no dielectric between the plates (C₀). For a Vaccume K = 1 and for air K = 1.0006 so we assume that are the same.

Question 22

current leakage

Answer 22

no real dielectric is a prefect insulator we ignoor this effect though.

Question 23

What happens when we insert a dielectric between the plates?

Also what happens to the charge density?

Answer 23

the PD between the paltes decreases by a factor of K e.g if E₀ is the electric field strength in a vaccume and E is the value with the dielectric E = E₀/K.

Since the electricfield magnitude is smaller when the dielectric is present the surface charge density must be smaller aswell.

Question 24

Why does the surface charge density change?

Answer 24

The surface charge on the conducting plates doesn’t change. Insted an induced charge of opposite sign appears on each surface of the dielectric (if the dielectric was origionally electrically nutral then it is still). The induced surface charge arrises as a result of the redistribution of positive and negative charge within the dielectric material, this is known as polarisation.

Question 25

How to derive a relation ship between the magnitude of the charge per unit area indused on a dielectric surface?

Answer 25

The magnitude of the surface charge density on the conductors is given by σ. The magnitude of the charge per unit area on the dielectric is given by σ_i. There for the net charge dencity is given by σ - σ_i.